Finite Group Databasebeta

← Group #10691179

Character table — Group #10691179

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11112222222222444444444444448888888888888888881212121216161616161616161616242424242424242424244848
order12222234444666444466121212121212121288888888121224242424242424242244441212121224242424248888888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111
χ51111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1
χ61111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111111111-1-1
χ91111111-1-1-1-111111-1-11111-1-1-1-1-1-1ii−i−iii−i−i1-1iiii−i−i−i−i11-1-11-111-1-1ii−i−i-11ii−i−iii−i−i1-1
χ101111111-1-1-1-111111-1-11111-1-1-1-1-1-1ii−i−iii−i−i1-1iiii−i−i−i−i-1-1111-111-1-1ii−i−i1-1−i−iii−i−iii-11
χ111111111-1-1-1-111111-1-11111-1-1-1-1-1-1ii−i−i−i−iii1-1−i−i−i−iiiii11-1-1-11-1-111ii−i−i-11ii−i−i−i−iii-11
χ121111111-1-1-1-111111-1-11111-1-1-1-1-1-1ii−i−i−i−iii1-1−i−i−i−iiiii-1-111-11-1-111ii−i−i1-1−i−iiiii−i−i1-1
χ131111111-1-1-1-111111-1-11111-1-1-1-1-1-1−i−iiiii−i−i1-1iiii−i−i−i−i11-1-1-11-1-111−i−iii-11−i−iiiii−i−i-11
χ141111111-1-1-1-111111-1-11111-1-1-1-1-1-1−i−iiiii−i−i1-1iiii−i−i−i−i-1-111-11-1-111−i−iii1-1ii−i−i−i−iii1-1
χ151111111-1-1-1-111111-1-11111-1-1-1-1-1-1−i−iii−i−iii1-1−i−i−i−iiiii11-1-11-111-1-1−i−iii-11−i−iii−i−iii1-1
χ161111111-1-1-1-111111-1-11111-1-1-1-1-1-1−i−iii−i−iii1-1−i−i−i−iiiii-1-1111-111-1-1−i−iii1-1ii−i−iii−i−i-11
χ1722222222222222-2-2-2-222-2-22222-2-200000000-2-20000000022220000000000-2-20000000000
χ1822222222222222-2-2-2-222-2-22222-2-200000000-2-200000000-2-2-2-20000000000220000000000
χ192222222-2-2-2-2222-2-22222-2-2-2-2-2-22200000000-220000000022-2-200000000002-20000000000
χ202222222-2-2-2-2222-2-22222-2-2-2-2-2-22200000000-2200000000-2-2220000000000-220000000000
χ21222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1000022-1-1-1-1-1-1-1-1000000000000
χ22222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-1-1111111110000-2-21111-1-1-1-1000000000000
χ23222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-10000-2-211111111000000000000
χ24222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-111111111000022-1-1-1-11111000000000000
χ25222222-1-2-2-2-2-1-1-122-2-2-1-1-1-11111112i2i−2i−2i2i2i−2i−2i-11−i−i−i−iiiii00002-2-1-111−i−iii000000000000
χ26222222-1-2-2-2-2-1-1-122-2-2-1-1-1-11111112i2i−2i−2i−2i−2i2i2i-11iiii−i−i−i−i0000-2211-1-1−i−iii000000000000
χ27222222-1-2-2-2-2-1-1-122-2-2-1-1-1-1111111−2i−2i2i2i2i2i−2i−2i-11−i−i−i−iiiii0000-2211-1-1ii−i−i000000000000
χ28222222-1-2-2-2-2-1-1-122-2-2-1-1-1-1111111−2i−2i2i2i−2i−2i2i2i-11iiii−i−i−i−i00002-2-1-111ii−i−i000000000000
χ292222-2-2222-2-22222-22-2-2-22222-2-2222i−2i2i−2i0000-2-20000000000000000002i−2i2i−2i000000000000
χ302222-2-2222-2-22222-22-2-2-22222-2-222−2i2i−2i2i0000-2-2000000000000000000−2i2i−2i2i000000000000
χ312222-2-2222-2-2222-22-22-2-2-2-222-2-2-2-200000000220000000000000000000000002i−2i2i−2i000000
χ322222-2-2222-2-2222-22-22-2-2-2-222-2-2-2-20000000022000000000000000000000000−2i2i−2i2i000000
χ332222-2-22-2-2222222-2-22-2-222-2-222-2-22-2-220000-220000000000000000002-2-22000000000000
χ342222-2-22-2-2222222-2-22-2-222-2-222-2-2-222-20000-22000000000000000000-222-2000000000000
χ352222-2-22-2-222222-222-2-2-2-2-2-2-22222000000002-20000000000000000000000002-2-22000000
χ362222-2-22-2-222222-222-2-2-2-2-2-2-22222000000002-2000000000000000000000000-222-2000000
χ372222-2-2-122-2-2-1-1-12-22-211-1-1-1-111-1-12i−2i2i−2i000011−i3−i3i3i3−i3−i3i3i30000003−33−3−ii−ii000000000000
χ382222-2-2-122-2-2-1-1-12-22-211-1-1-1-111-1-12i−2i2i−2i000011i3i3−i3−i3i3i3−i3−i3000000−33−33−ii−ii000000000000
χ392222-2-2-122-2-2-1-1-12-22-211-1-1-1-111-1-1−2i2i−2i2i000011−i3−i3i3i3−i3−i3i3i3000000−33−33i−ii−i000000000000
χ402222-2-2-122-2-2-1-1-12-22-211-1-1-1-111-1-1−2i2i−2i2i000011i3i3−i3−i3i3i3−i3−i30000003−33−3i−ii−i000000000000
χ412222-2-2-1-2-222-1-1-12-2-2211-1-111-1-1112-2-2200001-133−3−3−3−333000000−333−3-111-1000000000000
χ422222-2-2-1-2-222-1-1-12-2-2211-1-111-1-1112-2-2200001-1−3−33333−3−30000003−3−33-111-1000000000000
χ432222-2-2-1-2-222-1-1-12-2-2211-1-111-1-111-222-200001-133−3−3−3−3330000003−3−331-1-11000000000000
χ442222-2-2-1-2-222-1-1-12-2-2211-1-111-1-111-222-200001-1−3−33333−3−3000000−333−31-1-11000000000000
χ452-22-22-222i−2i2i−2i2-2-200002-2002i−2i2i−2i0000001+i−1−i1−i−1+i001+i−1−i1+i−1−i1−i−1+i1−i−1+i2-22i−2i00000000000000001+i−1−i1−i−1+i00
χ462-22-22-222i−2i2i−2i2-2-200002-2002i−2i2i−2i0000001+i−1−i1−i−1+i001+i−1−i1+i−1−i1−i−1+i1−i−1+i-22−2i2i0000000000000000−1−i1+i−1+i1−i00
χ472-22-22-222i−2i2i−2i2-2-200002-2002i−2i2i−2i000000−1−i1+i−1+i1−i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i2-22i−2i0000000000000000−1−i1+i−1+i1−i00
χ482-22-22-222i−2i2i−2i2-2-200002-2002i−2i2i−2i000000−1−i1+i−1+i1−i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i-22−2i2i00000000000000001+i−1−i1−i−1+i00
χ492-22-22-22−2i2i−2i2i2-2-200002-200−2i2i−2i2i0000001−i−1+i1+i−1−i001−i−1+i1−i−1+i1+i−1−i1+i−1−i2-2−2i2i00000000000000001−i−1+i1+i−1−i00
χ502-22-22-22−2i2i−2i2i2-2-200002-200−2i2i−2i2i0000001−i−1+i1+i−1−i001−i−1+i1−i−1+i1+i−1−i1+i−1−i-222i−2i0000000000000000−1+i1−i−1−i1+i00
χ512-22-22-22−2i2i−2i2i2-2-200002-200−2i2i−2i2i000000−1+i1−i−1−i1+i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i2-2−2i2i0000000000000000−1+i1−i−1−i1+i00
χ522-22-22-22−2i2i−2i2i2-2-200002-200−2i2i−2i2i000000−1+i1−i−1−i1+i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i-222i−2i00000000000000001−i−1+i1+i−1−i00
χ53444444-24444-2-2-2-4-4-4-4-2-222-2-2-2-22200000000220000000000000000000000000000000000
χ54444444-2-4-4-4-4-2-2-2-4-444-2-2222222-2-2000000002-20000000000000000000000000000000000
χ554444-4-4-244-4-4-2-2-2-44-442222-2-2222200000000-2-20000000000000000000000000000000000
χ564444-4-4-2-4-444-2-2-2-444-4222222-2-2-2-200000000-220000000000000000000000000000000000
χ574-44-44-4-24i−4i4i−4i-2220000-2200−2i2i−2i2i0000002+2i−2−2i2−2i−2+2i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000000000000000000000
χ584-44-44-4-24i−4i4i−4i-2220000-2200−2i2i−2i2i000000−2−2i2+2i−2+2i2−2i001+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000000000000000000000
χ594-44-44-4-2−4i4i−4i4i-2220000-22002i−2i2i−2i0000002−2i−2+2i2+2i−2−2i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000000000000000000000
χ604-44-44-4-2−4i4i−4i4i-2220000-22002i−2i2i−2i000000−2+2i2−2i−2−2i2+2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000000000000000000000
χ614-44-4-4444i−4i−4i4i4-4-40000-44004i−4i−4i4i0000000000000000000000000000000000000000000000
χ624-44-4-444−4i4i4i−4i4-4-40000-4400−4i4i4i−4i0000000000000000000000000000000000000000000000
χ634-44-4-44-24i−4i−4i4i-22200002-200−2i2i2i−2i000000000000−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ1100000000000000000000000000
χ644-44-4-44-24i−4i−4i4i-22200002-200−2i2i2i−2i000000000000ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ1100000000000000000000000000
χ654-44-4-44-2−4i4i4i−4i-22200002-2002i−2i−2i2i000000000000−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ1100000000000000000000000000
χ664-44-4-44-2−4i4i4i−4i-22200002-2002i−2i−2i2i000000000000ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ1100000000000000000000000000
χ6788-8-80080000-88-80000000000000000000000000000000000000000000000000000000000
χ6888-8-800-400004-4400000000000043−4300000000000000000000000000000000000000000000
χ6988-8-800-400004-44000000000000−434300000000000000000000000000000000000000000000
χ708-8-880080000-8-880000000000000000000000000000000000000000000000000000000000
χ718-8-8800-4000044-400000043−4300000000000000000000000000000000000000000000000000
χ728-8-8800-4000044-4000000−434300000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.